How much thrust is gained from placing a propeller in a duct?

Question

Assuming that the power and diameter are the same, how much extra thrust can be gained by placing a propeller in a duct? How does it influence the RPM?

To clarify: take any prop, place it in a well-designed duct, what can we expect? I expect higher RPM for same power, but also duct enhanced thrust. An approximation based on sources would be great.

Answer 1

Relative to MAV, as opposed to large scale rotors:

Compared to the baseline open rotor, the shrouded rotors showed increases in thrust by up to 94%, at the same power consumption, or reductions in power by up to 62% at the same thrust.

At rotor collectives above 10°, all shrouded-rotor models showed improvements in performance over the isolated (‘open’) rotor — that is, higher thrusts and lower power requirements. At the same power consumption, increases in thrust over the open rotor by up to 94% were observed, or, conversely, up to 49% reductions in power at the same thrust, for the condition where the open and shrouded rotors are required to have the same tip speed. If, instead, the rotor disk areas are required to be the same, then up to 90% increases in thrust at the same power.

The effects of changing any one of the four parameters (tip, rlip, d, Ld) on the shrouded-rotors’ performance became more pronounced as the other three parameters were changed to degrade the performance. It is therefore not possible to categorically state that any one particular parameter has a greater effect on performance than any other, since the amount of influence of any parameter depends on the values of the other parameters. The exception to this seems to be the lip radius, changes in which had almost same effect no 258 matter what the values of the other parameters are. Thus, in general, it would seem that changing the value of any shroud parameter so as to improve performance results in less sensitivity of the performance to changes in any of the other parameters; similarly, improving the efficiency of the rotor itself would seem to result in less of a performance benefit from the presence of a shroud.

Extracted from: HOVER AND WIND-TUNNEL TESTING OF SHROUDED ROTORS FOR IMPROVED MICRO AIR VEHICLE DESIGN Jason L. Pereira Doctor of Philosophy, 2008 Dissertation directed by: Professor Inderjit Chopra Department of Aerospace Engineering University of Maryland College Park

Rotor parameters including tip gaps, tilt and relative wind, collective, and motor characteristics will influence rotor RPM, and are indirectly addressed in Pereira's dissertation. Again, there are very broad assumptions in the OP question, but Pereira substantiates generalized efficiency improvements for specific configurations.

Answer 2

That "any prop" part is the killer. Most people get less thrust from trying that:

My experiments suggest only a a max of 20% improvement is possible:

It should spin slower (because more of the prop is producing lift, instead of stuck in the vortex at the tips) for the same power.

The "well designed" part of your question is also non-trivial - there's no such thing if you want the prop to perform optimally across a range of airspeeds - the duct has to be designed for a specific operating condition, so it will always make things worse at "off conditions" - which will usually be more worse than the prop without the duct.

The entire point of the duct is to reduce tip vortices, and the entire point of the tip region of "any propeller" is also to reduce vortices, so using both at once is not going to work properly, if at all (see video above - in real life, it does NOT work). The tips of a duct fan need to be totally different shape to the tips of "any propeller".

I question the accuracy of the paper mentioned: he shows that reduced diffuser angle improves thrust (p. 51 - but totally fails to consider Bernoulli for that, and never even tried angles less than 0 degrees), and his results and diagrams are almost all based on large diffuser angles, which is the opposite to Bernoulli, common sense, and modern practice.

In my relatively vast experience in this field, almost all CFD models and predictions are false (papers are usually written by students, none of whom understand modern ML techniques, especially the "time traveller conundrum" as it applies to CFD validation). Long story short - they do not realize that they're "training" their math to match the observations [almost always of poor experiments, and always of a tiny sample], instead of what the math is supposed to be - a prediction, for more than just the sample observed. Bottom line - if it's not something real that was measured, you can't trust the numbers.